Transient analysis of convexly constrained mixture methods

We study the transient performances of three convexly constrained adaptive combination methods that combine outputs of two adaptive filters running in parallel to model a desired unknown system. We propose a theoretical model for the mean and mean-square convergence behaviors of each algorithm. Specifically, we provide expressions for the time evolution of the mean and the variance of the combination parameters, as well as for the mean square errors. The accuracy of the theoretical models are illustrated through simulations in the case of a mixture of two LMS filters with different step sizes.